Ginsparg-Wilson fermions in odd dimensions
Ginsparg-Wilson fermions in odd dimensions
复制标题
奇数维的 Ginsparg-Wilson 费米子
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
J. Nishimura
中科院分区：
文献类型：
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作者：
W. Bietenholz;J. Nishimura
金斯帕-威尔逊关系，如果以适当的形式写成，也可以作为奇维无质量费米子的格点狄拉克算符的条件。费米子与这样一个狄拉克算子的作用量在广义宇称变换下是不变的，这在（朴素）连续极限下简化为普通宇称变换。然而，费米子测度在广义宇称变换下发生了非平凡的变换，因此宇称反常仅由费米子测度引起。类比的晶格建设手征规范理论在偶数维澄清考虑降维。我们还提出了一个自然的定义格Chern-Simons项，这是符合奇维Ginsparg-Wilson费米子。
The Ginsparg-Wilson relation, if written in a suitable form, can be used as a condition for lattice Dirac operators of massless fermions also in odd dimensions. The fermion action with such a Dirac operator is invariant under a generalized parity transformation, which reduces to the ordinary parity transformation in the (naive) continuum limit. The fermion measure, however, transforms non-trivially under the generalized parity transformation, and hence the parity anomaly arises solely from the fermion measure. The analogy to the lattice construction of chiral gauge theories in even dimensions is clarified by considering a dimensional reduction. We also propose a natural definition of a lattice Chern-Simons term, which is consistent with odd dimensional Ginsparg-Wilson fermions.